Uniform boundedness of critical crossing probabilities implies hyperscaling

✍ Scribed by C. Borgs; J. T. Chayes; H. Kesten; J. Spencer

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 324 KB
• Volume: 15
• Category: Article
• ISSN: 1042-9832
• DOI: 10.1002/(sici)1098-2418(199910/12)15:3/4<368::aid-rsa9>3.0.co;2-b

✦ Synopsis

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.